POLYNOMIAL DUAL NETWORK SIMPLEX ALGORITHMS

We show how to use polynomial and strongly polynomial capacity scaling algorithms for the transshipment problem to design a polynomial dual network simplex pivot rule. Our best pivoting strategy leads to an O(m2 log n) bound on the number of pivots, where n and m denotes the number of nodes and arcs in the input network. If the demands are integral and at most B, we also give an O(m(m+ n log n) min(log nB, m log n))-time implementation of a strategy that requires somewhat more pivots.